HP is the worst of them all. Disabling the whole multimachine because some random unidentified part no longer works is bust forcing people to replace otherwise functioning machines. I had a printer that support said could not be fixed, bit I wanted to keep using the scanner - not possible. Just buy a new one they said
It depends on the model but generally no. For using the scanner only, many of them will still allow use through USB. The screen on the printer itself won't allow you to until you replace ink or repair whatever printer fault if has. I recommend NAPS2 for PDF scanning.
There are too many models to reverse engineer them all (both hardware and firmware). HP has seriously invested in encryption to make sure you can only use new and genuine ink. It's not that it's unhackable, just that it's impractical to do so, especially when you can easily just buy from another brand.